How to create such 3D chaos?

Grasshopper
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please click the image to get a clear view.

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These are called strange attractors. You either use scripting (i.e. Python, C#, etc.) or an add-on that handles it for you.

In 2019, I’d implemented about 40 strange attractors in Python:

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I would recommend the Chimpanzee plug-in, which includes 2D chaotic maps and oscillators, 3D strange attractors, 4D hyperchaotic systems, etc.

In September there will be Chimpanzee 0.4 released with some major features update including escape-time fractals.

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See attached

Chaos_V4C.gh (124.4 KB)

PS: If you know C# you can very easily modify C# N3 ( for other “chaotic” stuff ).